Ed submits the following:
Suppose I am looking at a crowd of people and cry ‘there is a man in the crowd!’. Well very likely, and clearly I have some man in mind. But the predicate ‘is a man in the crowd’ is not just true of him, but of every man in the crowd. So what I have said is true of each of the men, at least in one sense of ‘true of’.
Yet on the other hand. I go on to say ‘he is wearing a red scarf’. And suppose three men are wearing red scarves. So what I say is true of just three men, but still more than one. Finally I say ‘the man is carrying a poster of Che’, and suppose only one red scarved man is carrying such a poster. So it is now clear who I am talking about. But wasn’t I talking about the same man all along? So in another sense of ‘true of’, my initial statement ‘there is a man in the crowd’ was true of just one man, namely the one in the red scarf, carrying the Che poster.
Difficult. It is this sort of consideration that led Sommers (and Brandom and Chastain and probably others) to suppose that some existentially quantified sentences ‘refer’. Geach disagreed, he had a famous and very bitter dispute with Sommers in the TLS, although I haven’t been able to find this.
You see a man in a crowd, wearing a red scarf, and carrying a poster of Che. You don't see some man or other, but a definite man, one and the same man singled out in a series of visual perceptions. You exclaim, 'There is a man in the crowd' and your utterance is true. Not only is it true, it records (part of) the content of your perception.
The problem, I take, it is to find a way to avoid the following contradiction: 'There is a man in the crowd' is about any man in the crowd and yet it is about exactly one man. (We are assuming that there is more than one man in the crowd.)
Perhaps something like the distinction between speaker's reference and semantic reference will help. I say to you: 'The man in the corner with champagne in his glass is the new dean.' I have managed to refer, successfully, to a particular man and draw your attention to him. Moreover, I have supplied you with a bit of correct information about him. And yet there is no man in the corner with champagne in his glass. For what there is in his glass is acqua minerale.
The reference has failed, and yet the reference has succeeded. Contradiction. Solution? The distinction just mentioned. The definite description 'The man in the corner with champagne is his glass' lacks a semantic referent which is to say: the definite description considered apart from the speaker and his intentions does not refer to anything since nothing satisfies it. But the description does have a speaker's (and a hearer's) referent.
Similarly, we can say that the existentially general sentence 'There is a man in the crowd,' considered by itself apart from the perceptual situation in which the speaker visually singles out a man with a red scarf holding a Che poster, is not about any particular man such as Manny Manischewitz. For it could just as well be about Kasimir Bonch-Osmolovsky or Giacomo Giacopuzzi. (All three gentlemen are in the crowd.) Absent this abstraction from the perceptual situation, however, the existentially general sentence is about the one definite man in the red scarf, etc.